Find m\angle Am∠Am, angle, A. Round to the nearest degree.
1 answer:
Answer:
m∠A = 106°
Step-by-step explanation:
All three sides of the triangle are given in the question.
To find the measure of included angle A between two sides we will apply cosine formula,
BC²= AB² + AC² - 2(AB)(AC)cosA
(13)² = (10)² + (6)² - 2(10)(6)cosA
169 = 100 + 36 - 120cosA
cosA =
cosA = -0.275
A =
A = 105.96°
A ≈ 106°
Therefore, m∠A = 106° will be the answer.
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<u>ANSWER: </u>
170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution to obtain 1870 liters of 60% solution.
<u>SOLUTION: </u>
First, set up a table. Fill in the unknowns with variables x and y. The table is attached below
From this, we can easily set up the two equations.
Sum of values of two acids = Value of mixture
0.1x + 0.65y = 1122
For convenience, we'll multiply the entire equation by 100,
10x + 65y = 112200 ------ (1)
Now, Sum of amounts of each acid = Amount of mixture
x + y = 1870 ---------(2)
multiply (2) with 10 for easy calculation and derive the equation into one variable.
10x + 10y = 18700
Subtracting equation (2) from (1),
( + ) 10x + 65y = 112200
( − ) 10x + 10y = 18700
we get the solution as,
0 + 55y = 93500
Thus, 55y = 93500
y = 1700
Substituting y = 1700 in (2),
x + 1700 = 1870
x = 1870 - 1700
x = 170
So, we have x = 170 and y = 1700
We can conclude that 170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution to obtain 1870 liters of 60% solution.
